# 9.  The heights of 10 girls were measured in cm and the results are as follows:        135, 150, 139, 128, 151, 132, 146, 149, 143, 141.  (i) What is the height of the tallest girl?(ii) What is the height of the shortest girl?   (iii) What is the range of the data? (iv) What is the mean height of the girls?    (v) How many girls have heights more than the mean height.

H Harsh Kankaria

Given,

Heights of 10 girls (in cm) =  $135, 150, 139, 128, 151, 132, 146, 149, 143, 141$

Arranging the above data in ascending order = $128, 132, 135, 139, 141, 143, 146, 149, 150, 151$

(i) Height of the tallest girl = $151\ cm$

(ii) Height of the shortest girl = $128\ cm$

(iii) Range of the data = $(151 -128)\ cm$

$= 23\ cm$

(iv)  We know, Arithmetic mean = $\frac{sum\ of\ observations}{number\ of\ observation}$

$\\ = \frac{128+ 132+ 135+ 139+ 141+ 143+ 146+ 149+ 150+ 151}{10} \\ = \frac{1414}{10} \\ \\ = 141.4\ cm$

Therefore, mean height of the girls is $141.4\ cm$

(iv) Here, mean height = $141.4\ cm$

And, $143, 146,149,150,151$ are more than $141.4$

Therefore, 5  girls have height more than the average height.

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